Do you use a VPN? It seems like the last month or two they've really gotten heavy handed with blocking users on VPNs and it manifests exactly as you described your initial issues. All you need to do if that's the case is change your VPN location until the game stops bothering you about authentication.

Now that you deleted everything it's a little trickier. Your data should be linked with some form of recoverable account- Apple, Google Play, Nintendo, etc. That would be whatever you linked it with when you created the account. Assuming the VPN thing is your issue it's just a matter of cycling through locations until the game will let you in, and then redownloading the data after logging in.